35,492 research outputs found
Dissipative Linear Stochastic Hamiltonian Systems
This paper is concerned with stochastic Hamiltonian systems which model a
class of open dynamical systems subject to random external forces. Their
dynamics are governed by Ito stochastic differential equations whose structure
is specified by a Hamiltonian, viscous damping parameters and
system-environment coupling functions. We consider energy balance relations for
such systems with an emphasis on linear stochastic Hamiltonian (LSH) systems
with quadratic Hamiltonians and linear coupling. For LSH systems, we also
discuss stability conditions, the structure of the invariant measure and its
relation with stochastic versions of the virial theorem. Using Lyapunov
functions, organised as deformed Hamiltonians, dissipation relations are also
considered for LSH systems driven by statistically uncertain external forces.
An application of these results to feedback connections of LSH systems is
outlined.Comment: 10 pages, 1 figure, submitted to ANZCC 201
Decoherence of adiabatically steered quantum systems
We study the effect of Markovian environmental noise on the dynamics of a
two-level quantum system which is steered adiabatically by an external driving
field. We express the master equation taking consistently into account all the
contributions to the lowest non-vanishing order in the coupling to the
Markovian environment. We study the master equation numerically and
analytically and we find that, in the adiabatic limit, a zero-temperature
environment does not affect the ground state evolution. As a physical
application, we discuss extensively how the environment affects Cooper pair
pumping. The adiabatic ground state pumping appears to be robust against
environmental noise. In fact, the relaxation due to the environment is required
to avoid the accumulation of small errors from each pumping cycle. We show that
neglecting the non-secular terms in the master equation leads to unphysical
results, such as charge non-conservation. We discuss also a possible way to
control the environmental noise in a realistic physical setup and its influence
on the pumping process.Comment: 13 pages, 11 figures. Final versio
Tailoring many-body entanglement through local control
We construct optimal time-local control pulses based on a multipartite
entanglement measure as target functional. The underlying control Hamiltonians
are derived in a purely algebraic fashion, and the resulting pulses drive a
composite quantum system rapidly into that highly entangled state which can be
created most efficiently for a given interaction mechanism, and which bears
entanglement that is robust against decoherence. Moreover, it is shown that the
control scheme is insensitive to experimental imperfections in first order.Comment: 12 pages, 11 figure
Stability, Gain, and Robustness in Quantum Feedback Networks
This paper concerns the problem of stability for quantum feedback networks.
We demonstrate in the context of quantum optics how stability of quantum
feedback networks can be guaranteed using only simple gain inequalities for
network components and algebraic relationships determined by the network.
Quantum feedback networks are shown to be stable if the loop gain is less than
one-this is an extension of the famous small gain theorem of classical control
theory. We illustrate the simplicity and power of the small gain approach with
applications to important problems of robust stability and robust
stabilization.Comment: 16 page
Fidelity of optimally controlled quantum gates with randomly coupled multiparticle environments
This work studies the feasibility of optimal control of high-fidelity quantum
gates in a model of interacting two-level particles. One particle (the qubit)
serves as the quantum information processor, whose evolution is controlled by a
time-dependent external field. The other particles are not directly controlled
and serve as an effective environment, coupling to which is the source of
decoherence. The control objective is to generate target one-qubit gates in the
presence of strong environmentally-induced decoherence and under physically
motivated restrictions on the control field. It is found that interactions
among the environmental particles have a negligible effect on the gate fidelity
and require no additional adjustment of the control field. Another interesting
result is that optimally controlled quantum gates are remarkably robust to
random variations in qubit-environment and inter-environment coupling
strengths. These findings demonstrate the utility of optimal control for
management of quantum-information systems in a very precise and specific
manner, especially when the dynamics complexity is exacerbated by inherently
uncertain environmental coupling.Comment: tMOP LaTeX, 9 pages, 3 figures; Special issue of the Journal of
Modern Optics: 37th Winter Colloquium on the Physics of Quantum Electronics,
2-6 January 200
Robust Mean Square Stability of Open Quantum Stochastic Systems with Hamiltonian Perturbations in a Weyl Quantization Form
This paper is concerned with open quantum systems whose dynamic variables
satisfy canonical commutation relations and are governed by quantum stochastic
differential equations. The latter are driven by quantum Wiener processes which
represent external boson fields. The system-field coupling operators are linear
functions of the system variables. The Hamiltonian consists of a nominal
quadratic function of the system variables and an uncertain perturbation which
is represented in a Weyl quantization form. Assuming that the nominal linear
quantum system is stable, we develop sufficient conditions on the perturbation
of the Hamiltonian which guarantee robust mean square stability of the
perturbed system. Examples are given to illustrate these results for a class of
Hamiltonian perturbations in the form of trigonometric polynomials of the
system variables.Comment: 11 pages, Proceedings of the Australian Control Conference, Canberra,
17-18 November, 2014, pp. 83-8
Noise spectroscopy of a quantum-classical environment with a diamond qubit
Knowing a quantum system's environment is critical for its practical use as a
quantum device. Qubit sensors can reconstruct the noise spectral density of a
classical bath, provided long enough coherence time. Here we present a protocol
that can unravel the characteristics of a more complex environment, comprising
both unknown coherently coupled quantum systems, and a larger quantum bath that
can be modeled as a classical stochastic field. We exploit the rich environment
of a Nitrogen-Vacancy center in diamond, tuning the environment behavior with a
bias magnetic field, to experimentally demonstrate our method. We show how to
reconstruct the noise spectral density even when limited by relatively short
coherence times, and identify the local spin environment. Importantly, we
demonstrate that the reconstructed model can have predictive power, describing
the spin qubit dynamics under control sequences not used for noise
spectroscopy, a feature critical for building robust quantum devices. At lower
bias fields, where the effects of the quantum nature of the bath are more
pronounced, we find that more than a single classical noise model are needed to
properly describe the spin coherence under different controls, due to the back
action of the qubit onto the bath.Comment: Main text: 5 pages, 5 figures. Supplemental material: 7 pages, 7
figures, 4 table
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